MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. MoneyGram offers an efficient, fast and secure way to send money around the world. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide.